List questions from connectedness

449

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Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

Published on 08 Mar 2018 - 18:47

98

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How to show connectedness?

Published on 25 Mar 2026 - 6:17

394

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Is "connected via simple chain" a transitive relation?

Published on 09 Mar 2018 - 14:54

87

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How to check continuous function $f$ has extension?

Published on 11 Mar 2018 - 14:52

594

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Compactness and connectedness of sets

Published on 12 Mar 2018 - 4:24

2.4k

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Minimum Number of Edges in $k$-connected Graph

Published on 12 Mar 2018 - 23:26

1k

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Connected Set in $ {R}^{2} $

Published on 14 Mar 2018 - 15:42

254

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Prob. 2, Sec. 23, in Munkres' TOPOLOGY, 2nd ed: If $J$ is a well-ordered set and if $\left\{ X_\alpha \right\}_{\alpha \in J}$ . . .

Published on 15 Mar 2018 - 13:42

1k

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Prove that if $G$ is $k$-connected, then the join $K_1 + G$ is $(k + 1)$-connected

Published on 16 Mar 2018 - 0:13

1.6k

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Prove that if $G$ is a $k$-edge-connected graph, then $G+K_1$ is $(k+1)$ -edge-connected (my proof)

Published on 16 Mar 2018 - 2:57

1.4k

Views

What is a minimal strongly connected component?

Published on 25 Mar 2026 - 6:19

162

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Which of the following sets are connected? NBHM 2018

Published on 18 Mar 2018 - 15:07

788

Views

Definition of disconnected?

Published on 19 Mar 2018 - 4:13

96

Views

Is below subspace is connected?

Published on 19 Mar 2018 - 12:05

71

Views

How to determine the floor of $\frac {x} {2}$

Published on 25 Mar 2026 - 6:04

List Question

Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

How to show connectedness?

Is "connected via simple chain" a transitive relation?

How to check continuous function $f$ has extension?

Compactness and connectedness of sets

Minimum Number of Edges in $k$-connected Graph

Connected Set in $ {R}^{2} $

Prob. 2, Sec. 23, in Munkres' TOPOLOGY, 2nd ed: If $J$ is a well-ordered set and if $\left\{ X_\alpha \right\}_{\alpha \in J}$ . . .

Prove that if $G$ is $k$-connected, then the join $K_1 + G$ is $(k + 1)$-connected

Prove that if $G$ is a $k$-edge-connected graph, then $G+K_1$ is $(k+1)$ -edge-connected (my proof)

What is a minimal strongly connected component?

Which of the following sets are connected? NBHM 2018

Definition of disconnected?

Is below subspace is connected?

How to determine the floor of $\frac {x} {2}$

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